Question

Qual a derivada de f(x) = cos (x⁵ - 7x)

Answer 1

Seja $u = x^5-7x$.

Logo, $f(u) = cos(u)$.

Portanto, pela regra de cadeia

$\frac{df}{dx} = \frac{df}{du}\cdot\frac{du}{dx} = -sin(u) \cdot (5x^4 - 7)$

$\frac{df}{dx}= -5x^4sin(x^5-7x) + 7sin(x^5-7x)$